How to loopcut a Square-based Pyramid?
Regardless it is square-based or not, you can always select all sloped edges, then hit W > Subdivide, then tweak the number of cuts as you want.



Another trick is to first bevel the pole vertex, with a very small value, to make all sloped faces quads (they might still look like triangles , but they are actually quads now), then you can use loop cut tool to cut them. After that, just remove the extra vertices with Remove Doubles tool.